How to repair sagging and chipped Celotex?

My 1954 Mackay in Palo Alto has a couple of Celotex problems, both being under the eaves of the house. In one place a Celotex panel is beginning to sag, and I wonder how to reattach it. Can the sagging piece be reattached using wood screws along the sagging edge? Is there wood backing behind each seam where Celotex panels meet? If there is no wood backing to screw into, what other method of repair is there? 
Second, there is a divot or hole (above a bathroom exhaust vent) that looks like it was dug by some small creature. What sort of material is appropriate to fill and smooth over that hole? Light weight spackle? Something else?
Thanks ahead of time for any suggestions. 
[img]https://i.postimg.cc/NKLf2YXH/B-sag-3.jpg[/img][/url]
[url=https://postimg.cc/DW6TxM1T][img]https://i.postimg.cc/DW6TxM1T/A-divit-1.jpg[/img][/url]
 
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